Simultaneous determination of mass parameter and radial marker in Schwarzschild geometry

We show that mass parameter and radial marker values can be indirectly measured in thought experiments performed in Schwarzschild spacetime, without using the Newtonian limit of general relativity or approximations based on Euclidean geometry. Our approach involves different proper time quantifications as well as solutions to systems of algebraic equations, and aims to strengthen the conceptual independence of general relativity from Newtonian gravity.

Analog Schwarzschild Black Hole from a Nonisentropic Fluid

We study the conditions under which an analog acoustic geometry of a relativistic fluid in flat spacetime can take the same form as the Schwarzschild black hole geometry. We find that the speed of sound must necessarily be equal to the speed of light. Since the speed of the fluid cannot exceed the speed of light, this implies that analog Schwarzschild geometry necessarily breaks down behind the horizon.

Geometric phase for Dirac Hamiltonian under gravitational fields in the nonrelativistic regime

We show the appearance of geometric phase in a Dirac particle traversing in nonrelativistic limit in a time-independent gravitational field. This turns out to be similar to the one originally described as a geometric phase in magnetic fields. We explore the geometric phase in the Kerr and Schwarzschild geometries, which have significant astrophysical implications. Nevertheless, the work can be extended to any spacetime background including that of time-dependent. In the Kerr background, i.e. around a rotating black hole, geometric phase reveals both the Aharonov–Bohm effect and Pancharatnam–Berry phase. However, in a Schwarzschild geometry, i.e. around a nonrotating black hole, only the latter emerges. We expect that our assertions can be validated in both the strong gravity scenarios, like the spacetime around black holes, and weak gravity environment around Earth.

Light Inextensible Strings (Thread) Under Tension in the Schwarzschild Geometry

Light inextensible string under tension is a stalwart feature of elementary physics. Here I show how considering such a string in the vicinity of a black hole, with the help of computer algebra systems, can generate insight into the Schwarzschild geometry in the context of an undergraduate homework problem. Light taut strings minimize their proper length, given by integrating the spatial component of the Schwarzschild metric along the string. The path itself is given by straightforward numerical solution to the Euler–Lagrange equations. If the string is entirely outside the event horizon, its closest approach to the singularity is tangential. At this point the string is visibly curved, surely a memorable and informative insight. The geometry of the Schwarzschild metric induces some interesting nonlocal phenomena: if the distance of closest approach is less than about [Formula: see text], the string self-intersects, even though it is everywhere under tension. Light taut strings furnish a third interpretation of the concept “straight line”, the other two being null geodesics and free-fall world lines. All the software used is available under the GPL.1

Painlevé–Gullstrand form of the Lense–Thirring Spacetime

The standard Lense–Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense–Thirring metric approaches the Kerr metric at large distances. Herein we shall discuss a specific variant of the standard Lense–Thirring metric, carefully chosen for simplicity, clarity, and various forms of improved mathematical and physical behaviour, (to be more carefully defined in the body of the article). We shall see that this Lense–Thirring variant can be viewed as arising from the linearization of a suitably chosen tetrad representing the Kerr spacetime. In particular, we shall construct an explicit unit-lapse Painlevé–Gullstrand variant of the Lense–Thirring spacetime, one that has flat spatial slices, a very simple and physically intuitive tetrad, and extremely simple curvature tensors. We shall verify that this variant of the Lense–Thirring spacetime is Petrov type I, (so it is not algebraically special), but nevertheless possesses some very straightforward timelike geodesics, (the “rain” geodesics). We shall also discuss on-axis and equatorial geodesics, ISCOs (innermost stable circular orbits) and circular photon orbits. Finally, we wrap up by discussing some astrophysically relevant estimates, and analyze what happens if we extrapolate down to small values of r; verifying that for sufficiently slow rotation we explicitly recover slowly rotating Schwarzschild geometry. This Lense–Thirring variant can be viewed, in its own right, as a “black hole mimic”, of direct interest to the observational astronomy community.

Isotropic Gravastar Model in Rastall Gravity

In the present paper, we have introduced a new model of gravastar with an isotropic matter distribution in Rastall gravity by the Mazur–Mottola (2004) mechanism. Mazur–Mottola approach is about the construction of gravastar which is predicted as an alternative to black hole. By following this convention, we define gravastar in the form of three phases. The first one is an interior phase which has negative density; the second part consists of thin shell comprising ultrarelativistic stiff fluid for which we have discussed the length, energy, and entropy. By the graphical analysis of entropy, we have shown that our proposed thin shell gravastar model is potentially stable. The third phase of gravastar is defined by the exterior Schwarzschild geometry. For the interior of gravastar, we have found the analytical solutions free from any singularity and the event horizon in the framework of Rastall gravity.

Knitting wormholes by entanglement in supergravity

We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of N extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $$ \mathcal{N} $$ N = 4 SU(2N) Super Yang-Mills theory in terms of a Higgsed SU(2N) → S(U(N) × U(N)) theory in which $$ \mathcal{O} $$ O (N2) degrees of freedom in each SU(N) sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.

On the symmetry and conservation law classification of the de Sitter–Schwarzschild metric and the corresponding wave and Klein–Gordon equations

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein–Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.