Metric of a regular rotating black hole or naked worm-hole. More...

#include <GyotoHayward.h>

Inheritance diagram for Gyoto::Metric::Hayward:

Public Types
typedef Gyoto::SmartPointer< Gyoto::SmartPointee >	Subcontractor_t(Gyoto::FactoryMessenger *, std::vector< std::string > const &)
	A subcontractor builds an object upon order from the Factory. More...

Public Member Functions
virtual Property const *	getProperties () const
	Get list of properties. More...

	Hayward ()
	Default constructor.

virtual Hayward *	clone () const
	Virtual copy constructor. More...

void	spin (const double spin)
	Set spin.

double	spin () const
	Returns spin.

void	charge (const double charge)
	Set charge.

double	charge () const
	Returns charge.

virtual double	getRms () const

virtual double	getRmb () const

virtual double	getSpecificAngularMomentum (double rr) const

virtual double	getPotential (double const pos[4], double l_cst) const

void	gmunu (double g[4][4], const double *pos) const

double	gmunu (const double *const x, int mu, int nu) const

void	gmunu_up (double gup[4][4], const double *pos) const

double	gmunu_up (const double *const x, int mu, int nu) const

int	christoffel (double dst[4][4][4], const double pos[4]) const
	Chistoffel symbol. More...

double	ScalarProd (const double pos[4], const double u1[4], const double u2[4]) const
	Scalar product. More...

virtual double	christoffel (const double coord[4], const int alpha, const int mu, const int nu) const
	Chistoffel symbol. More...

virtual int	christoffel (double dst[4][4][4], const double coord[4]) const
	Chistoffel symbol. More...

const std::string	kind () const
	Get kind_.

int	coordKind () const
	Get coordinate kind.

int	getRefCount ()

void	mass (const double)
	Set mass used in unitLength()

void	mass (const double, const std::string &unit)
	Set mass used in unitLength()

double	mass () const
	Get mass used in unitLength()

double	mass (const std::string &unit) const
	Get mass used in unitLength()

double	unitLength () const
	M * G / c^2, M is in kg, unitLength in meters. More...

double	unitLength (const std::string &unit) const
	unitLength expressed in specified unit

double	deltaMin () const

void	deltaMin (double h1)

double	deltaMax () const

virtual double	deltaMax (double const pos[8], double delta_max_external) const

void	deltaMax (double h1)

double	deltaMaxOverR () const
	Get delta_max_over_r_.

void	deltaMaxOverR (double t)
	Set delta_max_over_r_.

bool	keplerian () const
	Get keplerian_.

void	keplerian (bool)
	Set keplerian_.

virtual void	cartesianVelocity (double const coord[8], double vel[3])
	Compute xprime, yprime and zprime from 8-coordinates.

virtual double	SysPrimeToTdot (const double coord[4], const double v[3]) const
	Compute tdot as a function of dr/dt, dtheta/dt and dphi/dt. Everything is in geometrical units. More...

virtual void	circularVelocity (double const pos[4], double vel[4], double dir=1.) const
	Yield circular velocity at a given position. More...

virtual void	zamoVelocity (double const pos[4], double vel[4]) const
	Yield ZAMO velocity at a given position. More...

virtual void	nullifyCoord (double coord[8]) const
	Set tdot (coord[4]) such that coord is light-like. Everything is in geometrical units. More...

virtual void	nullifyCoord (double coord[8], double &tdot2) const
	Set tdot (coord[4]) such that coord is light-like and return other possible tdot. More...

virtual void	normalizeFourVel (double coord[8]) const
	Normalize fourvelvel to -1. More...

virtual void	normalizeFourVel (double const pos[4], double fourvel[4]) const
	Normalize fourvelvel to -1. More...

double	norm (const double pos[4], const double u1[4]) const
	Scalar product. More...

void	multiplyFourVect (double vect[4], double a) const
	multiply vector by scalar

void	addFourVect (double u1[4], double const u2[4]) const
	add second vector to first one

void	projectFourVect (double const pos[4], double u1[4], double const u2[4]) const
	project u1 orthogonally to u2 at pos

void	dualOneForm (double const IN_ARRAY1_1[4], double const IN_ARRAY1_2[4], double ARGOUT_ARRAY1[4]) const
	Computes dual 1-form Compute the dual 1-form of 4-vector. More...

virtual void	observerTetrad (obskind_t obskind, double const pos[4], double fourvel[4], double screen1[4], double screen2[4], double screen3[4]) const
	Computes the orthonormal local tetrad of the observer. More...

virtual void	observerTetrad (double const pos[4], double fourvel[4], double screen1[4], double screen2[4], double screen3[4]) const
	Computes the orthonormal local tetrad of the observer. More...

void	GramSchmidt (double const pos[4], double u0[4], double u1[4], double u2[4], double u3[4]) const
	Apply Gram-Schmidt orthonormalization to a basis. More...

virtual double	gmunu (double const x[4], int mu, int nu) const
	Metric coefficients. More...

virtual void	gmunu (double g[4][4], double const pos[4]) const
	Metric coefficients. More...

virtual int	myrk4 (Worldline *line, state_t const &coord, double h, state_t &res) const
	RK4 integrator. More...

virtual int	myrk4 (Worldline *line, const double coord[8], double h, double res[8]) const =delete
	Obsolete, update your code.

virtual int	myrk4_adaptive (Gyoto::Worldline *line, state_t const &coord, double lastnorm, double normref, state_t &coordnew, double h0, double &h1, double deltamax=GYOTO_DEFAULT_DELTA_MAX) const
	RK4 integrator with adaptive step. More...

virtual int	myrk4_adaptive (Gyoto::Worldline *line, const double coord[8], double lastnorm, double normref, double coordnew[8], double h0, double &h1, double deltamax=GYOTO_DEFAULT_DELTA_MAX) const =delete
	Obsolete, update your code.

virtual int	isStopCondition (double const coord[8]) const
	Check whether integration should stop. More...

virtual int	diff (state_t const &x, state_t &dxdt) const
	F function such as dx/dt=F(x,cst) More...

virtual int	diff (const double y[8], double res[8]) const =delete
	Obsolete, update your code.

virtual void	setParticleProperties (Gyoto::Worldline *line, double const coord[8]) const
	Set Metric-specific constants of motion. Used e.g. in KerrBL. More...

void	incRefCount ()
	Increment the reference counter. Warning: Don't mess with the counter.

int	decRefCount ()
	Decrement the reference counter and return current value. Warning: Don't mess with the counter.

virtual bool	isThreadSafe () const
	Whether this class is thread-safe. More...

void	set (Property const &p, Value val)
	Set Value of a Property.

void	set (Property const &p, Value val, std::string const &unit)
	Set Value (expressed in unit) of a Property.

void	set (std::string const &pname, Value val)
	Set Value of a Property.

void	set (std::string const &pname, Value val, std::string const &unit)
	Set Value (expressed in unit) of a Property.

Value	get (Property const &p) const
	Get Value of a Property.

Value	get (std::string const &pname) const
	Get Value of a Property.

Value	get (Property const &p, std::string const &unit) const
	Get Value of a Property, converted to unit.

Value	get (std::string const &pname, std::string const &unit) const
	Get Value of a Property, converted to unit.

Property const *	property (std::string const pname) const
	Find property by name. More...

virtual void	fillProperty (Gyoto::FactoryMessenger *fmp, Property const &p) const
	Output a single Property to XML. More...

virtual void	fillElement (Gyoto::FactoryMessenger *fmp) const
	Fill the XML element for this Object. More...

virtual void	setParameters (Gyoto::FactoryMessenger *fmp)
	Main loop for parsing Properties from XML description. More...

virtual int	setParameter (std::string name, std::string content, std::string unit)
	Set parameter by name. More...

virtual void	setParameter (Gyoto::Property const &p, std::string const &name, std::string const &content, std::string const &unit)
	Set parameter by Property (and name) More...

std::string	describeProperty (Gyoto::Property const &p) const
	Format desrciption for a property. More...

void	help () const
	Print (to stdout) some help on this class. More...

virtual void	hook (Listener *listener)
	Start listening. More...

virtual void	unhook (Listener *listener)
	Stop listening. More...

Static Public Attributes
static GYOTO_OBJECT Property const	properties []

Protected Member Functions
void	kind (const std::string)
	Set kind_. More...

void	coordKind (int coordkind)
	Set coordkind_. More...

virtual void	tellListeners ()
	Call tell() on each hooked Listener. More...

Protected Attributes
double	charge_
	Magnetic charge parameter.

double	spin_
	Angular momentum parameter.

double	a2_
	spin_*spin_

double	a3_
	a2_*spin_

double	a4_
	a2_*a2_

double	b2_
	charge_*charge_

double	delta_min_
	Minimum integration step for the adaptive integrator.

double	delta_max_
	Maximum integration step for the adaptive integrator.

double	delta_max_over_r_
	Numerical tuning parameter. More...

bool	keplerian_
	1 if circularVelocity should return the Newtonian Keplerian velocity, in r^-3/2

std::string	kind_
	The "kind" that is output in the XML entity. More...

std::vector< std::string >	plugins_
	The plug-ins that needs to be loaded to access this instance's class. More...

Private Attributes
double	mass_
	Mass yielding geometrical unit (in kg).

int	coordkind_
	Kind of coordinates (cartesian-like, spherical-like, unspecified)

int	refCount
	Reference counter.

pthread_mutex_t	mutex_
	A mutex. More...

ListenerItem *	listeners_
	Linked list of Listener items.

Friends
class	Gyoto::SmartPointer< Gyoto::Metric::Hayward >

Detailed Description

Metric of a regular rotating black hole or naked worm-hole.

This is a regular rotating extension of Hayward's metric.

The metric reads: ds^2=-(1-2*M(r)*r/Sigma)*dt^2-(4*a*M(r)*sin^2(theta)/Sigma)*dt*dphi+(Sigma/Delta)*dr^2+(Sigma)*dtheta^2+sin^2(theta)*[r^2+a^2+2*a^2*r*M(r)*sin^2(theta)/Sigma]*dphi^2, where: Sigma=r^2+a^2*cos^2(theta) Delta=r^2-2*M(r)*r+a^2 M(r)=M*abs(r)^3/(abs(r)^3+2*m*b^2), m being the mass of the black hole seen at infinity and b a magnetic charge parameter.

See Lamy et al. (2018), Classical and Quantum Gravity, submitted, https://arxiv.org/abs/1802.01635

See Hayward (2006) for the original nonrotating metric, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.031103

See Bambi & Modesto (2013) for a rotating (but singular) extension. https://www.sciencedirect.com/science/article/pii/S0370269313002505?via%3Dihub

Member Typedef Documentation

◆ Subcontractor_t

typedef Gyoto::SmartPointer< Gyoto::SmartPointee > Gyoto::SmartPointee::Subcontractor_t(Gyoto::FactoryMessenger *, std::vector< std::string > const &)

inherited

A subcontractor builds an object upon order from the Factory.

Various classes need to provide a subcontractor to be able to instantiate themselves upon order from the Factory. A subcontractor is a function (often a static member function) which accepts a pointer to a FactoryMessenger as unique parameter, communicates with the Factory using this messenger to read an XML description of the object to build, and returns this objet. SmartPointee::Subcontractor_t* is just generic enough a typedef to cast to and from other subcontractor types: Astrobj::Subcontractor_t, Metric::Subcontractor_t, Spectrum::Subcontractor_t. A subcontractor needs to be registered using the relevant Register() function: Astrobj::Register(), Metric::Register(), Spectrum::Register().

Member Function Documentation

◆ christoffel() [1/3]

virtual double Gyoto::Metric::Generic::christoffel	(	const double	coord[4],
		const int	alpha,
		const int	mu,
		const int	nu
	)		const

virtual

Chistoffel symbol.

Value of Christoffel symbol Γ^α_μν at point (x₁, x₂, x₃).

Reimplemented from Gyoto::Metric::Generic.

◆ christoffel() [2/3]

virtual int Gyoto::Metric::Generic::christoffel	(	double	dst[4][4][4],
		const double	coord[4]
	)		const

virtual

Chistoffel symbol.

Value of Christoffel symbol Γ^α_μν at point (x₁, x₂, x₃).

Returns: 1 on error, 0 otherwise

Reimplemented from Gyoto::Metric::Generic.

◆ christoffel() [3/3]

int Gyoto::Metric::Hayward::christoffel	(	double	dst[4][4][4],
		const double	coord[4]
	)		const

virtual

Chistoffel symbol.

Value of Christoffel symbol Γ^α_μν at point (x₁, x₂, x₃).

Returns: 1 on error, 0 otherwise

Reimplemented from Gyoto::Metric::Generic.

◆ circularVelocity()

virtual void Gyoto::Metric::Generic::circularVelocity	(	double const	pos[4],
		double	vel[4],
		double	dir = `1.`
	)		const

virtualinherited

Yield circular velocity at a given position.

Give the velocity of a massive particle in circular orbit at the given position projected onto the equatorial plane. Such a velocity may not exist everywhere (or anywhere) for a given metric. This method is intended to be used by Astrobj classes such as Torus or ThinDisk.

If keplerian_ is set to true, this method should return the Keplerian velcity instead (derived classes should ensure this, see KerrBL::circularVelocity() for instance).

The default implementation throws an error if keplerian_ is set to false.

Parameters

pos	input: position,
vel	output: velocity,
dir	1 for corotating, -1 for counterrotating.

Reimplemented in Gyoto::Metric::ChernSimons, Gyoto::Metric::KerrBL, Gyoto::Metric::KerrKS, and Gyoto::Metric::RezzollaZhidenko.

◆ clone()

virtual Hayward * Gyoto::Metric::Hayward::clone ( ) const

virtual

Virtual copy constructor.

Reimplemented from Gyoto::Metric::Generic.

◆ coordKind()

void Gyoto::Metric::Generic::coordKind ( int coordkind )

protectedinherited

Set coordkind_.

coordkind(int coordkind) is protected because, for most Metrics, it should not be changed in runtime. Set coordinate kind

◆ deltaMax() [1/3]

double Gyoto::Metric::Generic::deltaMax ( ) const

inherited

Get delta_max_

◆ deltaMax() [2/3]

virtual double Gyoto::Metric::Generic::deltaMax	(	double const	pos[8],
		double	delta_max_external
	)		const

virtualinherited

Get delta max at a given position

Parameters

pos	4-position
[optional]	delta_max_external external constraint on delta_max

Returns: the smallest value between delta_max_, delta_max_external, and R*delta_max_over_r_ where R is pos[1] in spherical coordinates and max(x1, x2, x3) in Cartesian coordinates.

◆ deltaMax() [3/3]

void Gyoto::Metric::Generic::deltaMax ( double h1 )

inherited

Set delta_max_

◆ deltaMin() [1/2]

double Gyoto::Metric::Generic::deltaMin ( ) const

inherited

Get delta_min_

◆ deltaMin() [2/2]

void Gyoto::Metric::Generic::deltaMin ( double h1 )

inherited

Set delta_min_

◆ describeProperty()

std::string Gyoto::Object::describeProperty ( Gyoto::Property const & p ) const

inherited

Format desrciption for a property.

Returns a string containing the name(s) and type of the property, as well as whether it supports unit.

◆ diff()

virtual int Gyoto::Metric::Generic::diff	(	state_t const &	x,
		state_t &	dxdt
	)		const

virtualinherited

F function such as dx/dt=F(x,cst)

Reimplemented in Gyoto::Metric::NumericalMetricLorene, and Gyoto::Metric::RotStar3_1.

◆ dualOneForm()

void Gyoto::Metric::Generic::dualOneForm	(	double const	IN_ARRAY1_1[4],
		double const	IN_ARRAY1_2[4],
		double	ARGOUT_ARRAY1[4]
	)		const

inherited

Computes dual 1-form Compute the dual 1-form of 4-vector.

Parameters

	IN_ARRAY1_1	4-position;
	IN_ARRAY1_2	quadrivector;
[out]	ARGOUT_ARRAY3	output 1-form

◆ fillElement()

virtual void Gyoto::Object::fillElement ( Gyoto::FactoryMessenger * fmp ) const

virtualinherited

Fill the XML element for this Object.

The base implementation simply calls fillProperty() for each Property defined for the Object.

Derived classes should avoid overriding fillElement(). It may make sense occasionally, e.g. to make sure that the metric is output first.

To customize how a given Property is rendered, it is better to override fillProperty().

If this method is overridden, the implementation should in general call fillElement() on the direct base.

Reimplemented in Gyoto::Astrobj::Complex, Gyoto::Spectrometer::Complex, and Gyoto::Scenery.

◆ fillProperty()

virtual void Gyoto::Object::fillProperty	(	Gyoto::FactoryMessenger *	fmp,
		Property const &	p
	)		const

virtualinherited

Output a single Property to XML.

The base implementation decides what to do based on the p.type. The format matches how setParameters() an setParameter() would interpret the XML descition.

Overriding this method should be avoided, but makes sense in some cases (for instance Screen::fillProperty() selects a different unit for Distance based on its magnitude, so that stellar sizes are expressed in solar radii while smaller sizes can be expressed in meters and larger sizes in parsecs).

Overriding implementation should fall-back on calling the implementation in the direct parent class:

class A: public Object {};
class B: public A { 
 using B::setParameter;
 virtual void fillProperty(Gyoto::FactoryMessenger *fmp,
                        Property const &p) const ;
};
void B::fillProperty(Gyoto::FactoryMessenger *fmp,
                        Property const &p) const {
  if (name=="Duff") fmp->doSomething();
  else A::fillProperty(fmp, p);
}

Reimplemented in Gyoto::Scenery, Gyoto::Astrobj::DirectionalDisk, Gyoto::Astrobj::Disk3D, Gyoto::Astrobj::EquatorialHotSpot, Gyoto::Astrobj::NeutronStarModelAtmosphere, Gyoto::Astrobj::PatternDisk, Gyoto::Astrobj::PolishDoughnut, Gyoto::Screen, Gyoto::Astrobj::Star, Gyoto::Spectrometer::Uniform, and Gyoto::Astrobj::XillverReflection.

◆ getPotential()

virtual double Gyoto::Metric::Hayward::getPotential	(	double const	pos[4],
		double	l_cst
	)		const

virtual

Returns potential W=-ln(|u_t|) for a cst specific angular momentum l_cst Should be implemented in derived classes if useful If called on the base class, returns an error

Reimplemented from Gyoto::Metric::Generic.

◆ getProperties()

virtual Property const * Gyoto::Metric::Hayward::getProperties ( ) const

virtual

Get list of properties.

This method is declared automatically by the GYOTO_OBJECT macro and defined automatically by the GYOTO_PROPERTY_END macro.

Reimplemented from Gyoto::Metric::Generic.

◆ getRmb()

virtual double Gyoto::Metric::Hayward::getRmb ( ) const

virtual

Returns the marginally bound radius Should be implemented in derived classes if useful If called on the base class, returns an error

Reimplemented from Gyoto::Metric::Generic.

◆ getRms()

virtual double Gyoto::Metric::Hayward::getRms ( ) const

virtual

Returns the marginally stable (ISCO) radius Should be implemented in derived classes if useful If called on the base class, returns an error

Reimplemented from Gyoto::Metric::Generic.

◆ getSpecificAngularMomentum()

virtual double Gyoto::Metric::Hayward::getSpecificAngularMomentum ( double rr ) const

virtual

Returns the specific angular momentum l=-u_phi/u_t Should be implemented in derived classes if useful If called on the base class, returns an error

Reimplemented from Gyoto::Metric::Generic.

◆ gmunu() [1/2]

virtual double Gyoto::Metric::Generic::gmunu	(	double const	x[4],
		int	mu,
		int	nu
	)		const

virtualinherited

Metric coefficients.

The default implementation calls Metric:: gmunu(double g[4][4], const double * pos) const

Parameters

x	4-position at which to compute the coefficient;
mu	1st index of coefficient, 0≤μ≤3;
nu	2nd index of coefficient, 0≤ν≤3;

Returns: Metric coefficient g_μ,ν at point x

Reimplemented in Gyoto::Metric::KerrKS, Gyoto::Metric::Minkowski, Gyoto::Metric::NumericalMetricLorene, and Gyoto::Metric::NumericalMetricLorene.

◆ gmunu() [2/2]

virtual void Gyoto::Metric::Generic::gmunu	(	double	g[4][4],
		double const	pos[4]
	)		const

virtualinherited

Metric coefficients.

The default implementation calls double gmunu(const double * x, int mu, int nu) const.

Parameters

[out]	g	4x4 array to store the coeefficients
[in]	x	4-position at which to compute the coefficients;

Returns: Metric coefficient g_μ,ν at point x

Reimplemented in Gyoto::Metric::KerrKS, Gyoto::Metric::Minkowski, and Gyoto::Metric::NumericalMetricLorene.

◆ GramSchmidt()

void Gyoto::Metric::Generic::GramSchmidt	(	double const	pos[4],
		double	u0[4],
		double	u1[4],
		double	u2[4],
		double	u3[4]
	)		const

inherited

Apply Gram-Schmidt orthonormalization to a basis.

On input, u0 to u3 must be four non-zero norm, independent 4-vectors. On output, they will form an orthonormal basis.

Parameters

[in]	pos	position,
[in,out]	u0	basis vector
[in,out]	u1	basis vector
[in,out]	u2	basis vector
[in,out]	u3	basis vector

◆ help()

void Gyoto::Object::help ( ) const

inherited

Print (to stdout) some help on this class.

Describe all properties that this instance supports.

◆ hook()

virtual void Gyoto::Hook::Teller::hook ( Listener * listener )

virtualinherited

Start listening.

Use from a Hook::Listener object method:

teller->hook(this)

where "this" is a Listener and "teller" is a Teller.

Use unhook() later to stop listening to a given Teller.

Parameters

listener pointer to the new listener

◆ isStopCondition()

virtual int Gyoto::Metric::Generic::isStopCondition ( double const coord[8] ) const

virtualinherited

Check whether integration should stop.

The integrating loop will ask this the Metric through this method whether or not it is happy to continue the integration. Typically, the Metric should answer 0 when everything is fine, 1 when too close to the event horizon, inside the BH...

Parameters

coord 8-coordinate vector to check.

◆ isThreadSafe()

virtual bool Gyoto::Object::isThreadSafe ( ) const

virtualinherited

Whether this class is thread-safe.

Return True if this object is thread-safe, i.e. if an instance and its clone can be used in parallel threads (in the context of Scenery::raytrace()). Known objects which are not thread-safe include Lorene metrics and everything from the Python plug-in.

The default implementation considers that the class itself is thread safe and recurses into the declared properties to check whether they are safe too. Classes that abide to the Object/Property paradigm and are themselves thread-safe have nothing special to do.

Objects that clone children in their copy constructor that are not declared as properties must take these children into account.

Classes that are never thread-safe must declare it. It acn be easily done using GYOTO_OBJECT_THREAD_SAFETY in the class declaration and GYOTO_PROPERTY_THREAD_UNSAFE in the class definition.

◆ kind()

void Gyoto::Metric::Generic::kind ( const std::string )

protectedinherited

Set kind_.

kind(const std::string) is protected because, for most Metrics, it should not be changed in runtime. Set kind_

◆ myrk4()

virtual int Gyoto::Metric::Generic::myrk4	(	Worldline *	line,
		state_t const &	coord,
		double	h,
		state_t &	res
	)		const

virtualinherited

RK4 integrator.

Reimplemented in Gyoto::Metric::KerrBL, and Gyoto::Metric::NumericalMetricLorene.

◆ myrk4_adaptive()

virtual int Gyoto::Metric::Generic::myrk4_adaptive	(	Gyoto::Worldline *	line,
		state_t const &	coord,
		double	lastnorm,
		double	normref,
		state_t &	coordnew,
		double	h0,
		double &	h1,
		double	deltamax = `GYOTO_DEFAULT_DELTA_MAX`
	)		const

virtualinherited

RK4 integrator with adaptive step.

Reimplemented in Gyoto::Metric::KerrBL, Gyoto::Metric::NumericalMetricLorene, and Gyoto::Metric::RotStar3_1.

◆ norm()

double Gyoto::Metric::Generic::norm	(	const double	pos[4],
		const double	u1[4]
	)		const

inherited

Scalar product.

Compute the norm of the quadrivector u1 in this Metric, at point pos expressed in coordinate system sys.

Parameters

[in]	pos	4-position;
[in]	u1	quadrivector;

Returns: ||u1||

◆ normalizeFourVel() [1/2]

virtual void Gyoto::Metric::Generic::normalizeFourVel	(	double const	pos[4],
		double	fourvel[4]
	)		const

virtualinherited

Normalize fourvelvel to -1.

First computes threevel as xiprime=xidot/x0dot for i in {1, 2, 3}, then computes x0dot using SyPrimeToTdot, then computes again xidot as xidot=xiprime*x0dot.

Parameters

[in]	pos	4-position;
[in,out]	fourvel	4-velocity, will be renormalized.

◆ normalizeFourVel() [2/2]

virtual void Gyoto::Metric::Generic::normalizeFourVel ( double coord[8] ) const

virtualinherited

Normalize fourvelvel to -1.

First computes threevel as xiprime=xidot/x0dot for i in {1, 2, 3}, then computes x0dot using SyPrimeToTdot, then computes again xidot as xidot=xiprime*x0dot.

Parameters

[in,out] coord 8-position, coord[4-7] will be set according to the other elements;

◆ nullifyCoord() [1/2]

virtual void Gyoto::Metric::Generic::nullifyCoord ( double coord[8] ) const

virtualinherited

Set tdot (coord[4]) such that coord is light-like. Everything is in geometrical units.

Set coord[4] so that the 4-velocity coord[4:7] is lightlike, i.e. of norm 0. There may be up to two solutions. coord[4] is set to the hightest. The lowest can be retrieved using nullifyCoord(double coord[8], double& tdot2) const. Everything is expressed in geometrical units.

Parameters

[in,out] coord 8-position, coord[4] will be set according to the other elements;

Reimplemented in Gyoto::Metric::KerrBL.

◆ nullifyCoord() [2/2]

virtual void Gyoto::Metric::Generic::nullifyCoord	(	double	coord[8],
		double &	tdot2
	)		const

virtualinherited

Set tdot (coord[4]) such that coord is light-like and return other possible tdot.

Set coord[4] so that the 4-velocity coord[4:7] is lightlike, i.e. of norm 0. There may be up to two solutions. coord[4] is set to the hightest. The lowest can be retrieved in tdot2. Everything is expressed in geometrical units.

Parameters

[in,out]	coord	8-position, coord[4] will be set according to the other elements;
[out]	tdot2	will be set to the smallest solution

Reimplemented in Gyoto::Metric::KerrBL.

◆ observerTetrad() [1/2]

virtual void Gyoto::Metric::Generic::observerTetrad	(	double const	pos[4],
		double	fourvel[4],
		double	screen1[4],
		double	screen2[4],
		double	screen3[4]
	)		const

virtualinherited

Computes the orthonormal local tetrad of the observer.

Parameters

[in]	pos	position,
[in]	fourvel	observer 4-velocity (norm -1)
[out]	screen1	first vector in the screen plane
[out]	screen2	second vector in the screen plane
[out]	screen3	vector normal to the screen

Reimplemented in Gyoto::Metric::KerrBL.

◆ observerTetrad() [2/2]

virtual void Gyoto::Metric::Generic::observerTetrad	(	obskind_t	obskind,
		double const	pos[4],
		double	fourvel[4],
		double	screen1[4],
		double	screen2[4],
		double	screen3[4]
	)		const

virtualinherited

Computes the orthonormal local tetrad of the observer.

Parameters

obskind	input: kind of observer (eg: "ZAMO","KeplerianObserver"...)
pos	input: position,
fourvel	output: observer 4-velocity (norm -1)
screen1	output: first vector in the screen plane
screen2	output: second vector in the screen plane
screen3	output: vector normal to the screen

Reimplemented in Gyoto::Metric::Minkowski.

◆ property()

Property const * Gyoto::Object::property ( std::string const pname ) const

inherited

Find property by name.

Look into the Property list for a Property whose name (or name_false, for a boolean Property) is pname. Return a const pointer to the first such property found, or NULL if none is found.

◆ ScalarProd()

double Gyoto::Metric::Hayward::ScalarProd	(	const double	pos[4],
		const double	u1[4],
		const double	u2[4]
	)		const

virtual

Scalar product.

Compute the scalarproduct of the two quadrivectors u1 and u2 in this Metric, at point pos expressed in coordinate system sys.

Parameters

pos	4-position;
u1	1st quadrivector;
u2	2nd quadrivector;

Returns: u1*u2

Reimplemented from Gyoto::Metric::Generic.

◆ setParameter() [1/2]

virtual void Gyoto::Object::setParameter	(	Gyoto::Property const &	p,
		std::string const &	name,
		std::string const &	content,
		std::string const &	unit
	)

virtualinherited

Set parameter by Property (and name)

This function is used when parsing an XML description, if Property (p) of this name is found (i.e. either p.name or p.name_false is equal to name). Implementation should fall-back on calling the direct's parent implementation:

class A: public Object {};
class B: public A { 
 using B::setParameter;
 virtual void setParameter(Gyoto::Property const &p,
                           std::string name,
                        std::string content,
                        std::string unit);
};
void B::setParameter(Gyoto::Property const &p,
                          std::string name,
                  std::string content,
                  std::string unit) {
  if (name=="Duff") doSomething(content, unit);
  else A::setParameter(p, name, content, unit);
}

Parameters

p	Property that matches name (p.name == name or p.name_false == name)
name	XML name of the parameter (XML entity)
content	string representation of the value
unit	string representation of the unit

Reimplemented in Gyoto::Astrobj::PolishDoughnut.

◆ setParameter() [2/2]

virtual int Gyoto::Object::setParameter	(	std::string	name,
		std::string	content,
		std::string	unit
	)

virtualinherited

Set parameter by name.

This function is used when parsing an XML description, if no Property of this name is found. Overriding implementation should fall-back on calling the direct's parent implementation:

class A: public Object {};
class B: public A { 
 using B::setParameter;
 virtual int setParameter(std::string name,
                    std::string content,
                    std::string unit);
};
int B::setParameter(std::string name,
                    std::string content,
                    std::string unit) {
  if (name=="Duff") doSomething(content, unit);
  else return A::setParameter(name, content, unit);
  return 0;  // name was known
}

Parameters

name	XML name of the parameter (XML entity). This may have a path component, e.g. "Astrobj::Radius", in which case a property named "Astrobj" will be sought in the current object, and setParameter will be called recusrively on this Astrobj with Radius as name.
content	string representation of the value
unit	string representation of the unit

Returns: 0 if this parameter is known, 1 if it is not.

Reimplemented in Gyoto::Astrobj::EquatorialHotSpot, Gyoto::Metric::KerrKS, Gyoto::Astrobj::Star, and Gyoto::Metric::RotStar3_1.

◆ setParameters()

virtual void Gyoto::Object::setParameters ( Gyoto::FactoryMessenger * fmp )

virtualinherited

Main loop for parsing Properties from XML description.

 This function queries the FactoryMessenger for elements to parse,
 and tries to matche each element to a Property to set it
 accordingly.

 Any class that tries to be buildable from XML must supply a
 subcontractor (for base classes such as Metric, Astrobj, Spectrum
 and Spectrometer, it is done as a template that must be
 specialized for each class).

 This subcontractor typically looks somewhat like this:

SmartPointer<Metric::Generic>
Gyoto::Metric::MyKind::Subcontractor(FactoryMessenger* fmp) {
  SmartPointer<MyKind> gg = new MyKind();
  gg -> setParameters(fmp);
  return gg;
}

 Although this is discouraged, it is possible to override the
 following functions to customize how XML entities are parsed:
   - setParameters() if low-level access to the
     FactoryMessenger is required;
   - setParameter(std::string name,
                  std::string content,
                  std::string unit)
     to interpret an entity that does not match a Property
     (e.g. alternative name);
   - setParameter(Gyoto::Property const &p,
                  std::string const &name,
                  std::string const &content,
                  std::string const &unit)
     to change how a Property is interpreted.

Reimplemented in Gyoto::Astrobj::Generic, Gyoto::Astrobj::Complex, Gyoto::Spectrometer::Complex, Gyoto::Astrobj::EquatorialHotSpot, Gyoto::Photon, Gyoto::Astrobj::Star, Gyoto::Spectrometer::Uniform, and Gyoto::Astrobj::OscilTorus.

◆ setParticleProperties()

virtual void Gyoto::Metric::Generic::setParticleProperties	(	Gyoto::Worldline *	line,
		double const	coord[8]
	)		const

virtualinherited

Set Metric-specific constants of motion. Used e.g. in KerrBL.

Reimplemented in Gyoto::Metric::NumericalMetricLorene.

◆ SysPrimeToTdot()

virtual double Gyoto::Metric::Generic::SysPrimeToTdot	(	const double	coord[4],
		const double	v[3]
	)		const

virtualinherited

Compute tdot as a function of dr/dt, dtheta/dt and dphi/dt. Everything is in geometrical units.

Parameters

coord	4-position (geometrical units);
v	3-velocity dx1/dx0, dx2/dx0, dx3/dx0;

Returns: tdot = dx0/dtau.

◆ tellListeners()

virtual void Gyoto::Hook::Teller::tellListeners ( )

protectedvirtualinherited

Call tell() on each hooked Listener.

Whenever a Teller mutates, it should warn any Listener hooked to it using tellListeners().

◆ unhook()

virtual void Gyoto::Hook::Teller::unhook ( Listener * listener )

virtualinherited

Stop listening.

Use from a Hook::Listener object method:

teller->unhook(this)

where "this" is a Listener, "teller" is a Teller, and "this" has called teller->hook(this) previously.

Parameters

listener pointer to the listener

◆ unitLength()

double Gyoto::Metric::Generic::unitLength ( ) const

inherited

M * G / c^2, M is in kg, unitLength in meters.

Metrics implementations are free to express lengths and distances in whatever unit they see fit (presumably most often geometrical units). This function returns this unit in SI (meters).

◆ zamoVelocity()

virtual void Gyoto::Metric::Generic::zamoVelocity	(	double const	pos[4],
		double	vel[4]
	)		const

virtualinherited

Yield ZAMO velocity at a given position.

Give the velocity of a zero angular momentul observer (whatever is closest to "at rest"). The default implementation simply projects (1, 0, 0, 0) othogonally along ephi and normalizes it, thus ensuring that vel is orthogonal to ephi.

Parameters

pos	input: position,
vel	output: velocity,

Reimplemented in Gyoto::Metric::KerrBL.

Member Data Documentation

◆ delta_max_over_r_

double Gyoto::Metric::Generic::delta_max_over_r_

protectedinherited

Numerical tuning parameter.

Ensure that delta (the numerical integration step) is never larger than a fraction of the distance between the current location and the center of the coordinate system.

For investigations close to the event horizon, 0.5 is usually fine. If high accuracy is needed long after deflection (weak lensing), then this must be smaller. A good test is to look at a MinDistance map for a FixedStar: it must be smooth.

◆ kind_

std::string Gyoto::Object::kind_

protectedinherited

The "kind" that is output in the XML entity.

E.g. for an Astrobj, fillElement() will ensure

Gyoto::Metric::Generic::kind

const std::string kind() const

Get kind_.

is written.

◆ mutex_

pthread_mutex_t Gyoto::SmartPointee::mutex_

privateinherited

A mutex.

When compiled with libpthread

◆ plugins_

std::vector<std::string> Gyoto::Object::plugins_

protectedinherited

The plug-ins that needs to be loaded to access this instance's class.

E.g. for an Astrobj, fillElement() will ensure

is written.

The documentation for this class was generated from the following file:

GyotoHayward.h

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Subcontractor_t

Member Function Documentation

◆ christoffel() [1/3]

◆ christoffel() [2/3]

◆ christoffel() [3/3]

◆ circularVelocity()

◆ clone()

◆ coordKind()

◆ deltaMax() [1/3]

◆ deltaMax() [2/3]

◆ deltaMax() [3/3]

◆ deltaMin() [1/2]

◆ deltaMin() [2/2]

◆ describeProperty()

◆ diff()

◆ dualOneForm()

◆ fillElement()

◆ fillProperty()

◆ getPotential()

◆ getProperties()

◆ getRmb()

◆ getRms()

◆ getSpecificAngularMomentum()

◆ gmunu() [1/2]

◆ gmunu() [2/2]

◆ GramSchmidt()

◆ help()

◆ hook()

◆ isStopCondition()

◆ isThreadSafe()

◆ kind()

◆ myrk4()

◆ myrk4_adaptive()

◆ norm()

◆ normalizeFourVel() [1/2]

◆ normalizeFourVel() [2/2]

◆ nullifyCoord() [1/2]

◆ nullifyCoord() [2/2]

◆ observerTetrad() [1/2]

◆ observerTetrad() [2/2]

◆ property()

◆ ScalarProd()

◆ setParameter() [1/2]

◆ setParameter() [2/2]

◆ setParameters()

◆ setParticleProperties()

◆ SysPrimeToTdot()

◆ tellListeners()

◆ unhook()

◆ unitLength()

◆ zamoVelocity()

Member Data Documentation

◆ delta_max_over_r_

◆ kind_

◆ mutex_

◆ plugins_