Gravitational energy in spherical symmetry

Penrose Inequality as a Constraint on the Low Energy Limit of Quantum Gravity

We construct initial data violating the anti-de Sitter Penrose inequality using scalars with various potentials. Since a version of the Penrose inequality can be derived from AdS/CFT, we argue that it is a new swampland condition, ruling out holographic UV completion for theories that violate it. We produce exclusion plots on scalar couplings violating the inequality, and we find no violations for potentials from string theory. In the special case where the dominant energy condition holds, we use general relativity techniques to prove the anti-de Sitter (AdS) Penrose inequality in all dimensions, assuming spherical, planar, or hyperbolic symmetry. However, our violations show that this result cannot be generically true with only the null energy condition, and we give an analytic sufficient condition for violation of the Penrose inequality, constraining couplings of scalar potentials. Like the Breitenlohner-Freedman bound, this gives a necessary condition for the stability of asymptotically AdS (AAdS) spacetimes.

Semiclassical relativistic stars

We present strong evidence that semiclassical gravity can give place to self-consistent ultracompact stars beyond the Buchdahl limit. We integrate the semiclassical equations of (spherically symmetric) stellar equilibrium for a constant-density classical fluid. The semiclassical contribution is modelled by a quantum massless scalar field in the only static vacuum state compatible with asymptotic flatness (Boulware vacuum). The Renormalized Stress-Energy Tensor (RSET) is firstly approximated by the analytic Polyakov approximation. This already reveals a crucial difference with respect to purely classical solutions: stars with compactness close to that of a black hole exhibit bounded pressures and curvatures up to a very small central core compared with the star radius. This suggests that a more refined approximation to the RSET at the core may give rise to strictly regular configurations. Following this suggestion, we prove that a minimal deformation of the Polyakov approximation inside the central core is sufficient to produce regular ultracompact stellar configurations.

The Black Hole Universe, Part I

The original Friedmann (1922) and Lemaitre (1927) cosmological model corresponds to a classical solution of General Relativity (GR), with the same uniform (FLRW) metric as the standard cosmology, but bounded to a sphere of radius R and empty space outside. We study the junction conditions for R to show that a co-moving observer, like us, located anywhere inside R, measures the same background and has the same past light-cone as an observer in an infinite FLRW with the same density. We also estimate the mass M inside R and show that in the observed universe R<rS≡2 GM, which corresponds to a Black Hole Universe (BHU). We argue that this original Friedmann–Lemaitre model can explain the observed cosmic acceleration without the need of Dark Energy, because rS acts like a cosmological constant Λ=3/rS2. The same solution can describe the interior of a stellar or galactic BHs. In co-moving coordinates the BHU is expanding while in physical or proper coordinates it is asymptotically static. Such frame duality corresponds to a simple Lorentz transformation. The BHU therefore provides a physical BH solution with an asymptotically deSitter metric interior that merges into a Schwarzschild metric exterior without discontinuities.

Geometry of static w = - 1 / 5 perfect fluid spheres in general relativity

We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state P = - ρ / 5 . These geometries depend on up to four parameters and are static and spherically symmetric. They describe compact spaces with naked central singularities.

Dynamics of Spontaneous Black Hole Scalarization and Mergers in Einstein-Scalar-Gauss-Bonnet Gravity

We study the dynamics of black holes in scalar Einstein-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, nonperturbative equations of motion. For one sign of the coupling parameter, nonspinning vacuum black holes are unstable to developing scalar hair, while for the other, instability only sets in for black holes with sufficiently large spin. We study scalarization in both cases, demonstrating that there is a range of parameter space where the theory maintains hyperbolic evolution and for which the instability saturates in a scalarized black hole that is stable without symmetry assumptions. However, this parameter space range is significantly smaller than the range for which stationary scalarized black hole solutions exist. We show how different choices for the subleading behavior of the Gauss-Bonnet coupling affect the dynamics of the instability and the final state, or lack thereof. Finally, we present mergers of binary black holes and demonstrate the imprint of the scalar hair in the gravitational radiation.

Unsettling Physics in the Quantum-Corrected Schwarzschild Black Hole

We study a quantum-corrected Schwarzschild black hole proposed recently in Loop Quantum Gravity. Prompted by the fact that corrections to the innermost stable circular orbit of Schwarzschild diverge, we investigate time-like and null radial geodesics. Massive particles moving radially outwards are confined, while photons make it to infinity with infinite redshift. This unsettling physics, which deviates radically from both Schwarzschild (near the horizon) and Minkowski (at infinity) is due to repulsion by the negative quantum energy density that makes the quasilocal mass vanish as one approaches spatial infinity.

Mathematical modelling and analysis of gravitational collapse in curved geometry

BACKGROUND AND OBJECTIVES

In the visible universe, it is believed that mass and energy are interchangeable. However, the physical and chemical processes in the hidden world put the scientist into the thought of matter and energy contents that are responsible for these phenomena. These are regarded as dark matter and dark energy. In this article, we study the effects of spacetime curvature on the gravitational collapse of dark energy in modified gravity, considering the collapse of the spherically symmetric star, which is composed of perfect and homogeneous fluid. We studied the collapse for closed, flat and hyperbolic geometry.

METHOD

As a result of mathematical modeling, we achieved highly non-linear differential equations. For the solution, we needed the assumption of physical significance. Specifically, we have taken the dark energy collapse. Then we achieved a simple system and solved for the analytic solutions of the field equations.

RESULTS

It is shown that the possible collapse is visibly influenced by spatial curvature. The collapse time is advanced for closed spacetime, delayed for the hypersurface, and the flat space behaves intermediately. We have taken here the equation of state in linear form to discuss the exhibition of fluid profile and a specific necessary criterion for the occurrence of spacetime singularity.

CONCLUSION

In this paper, we study the mathematical model of gravitational collapse in modified gravity, which derives the field equations using the principle of least action. The significant outcomes are the influences of the spatial curvature on the collapsing process and the time of formation of spacetime singularity. The matching of boundary and the fundamental continuity of the 1-form and 2-form are discussed.

Interpretational conflicts between the static and non-static forms of the de Sitter metric

The de-Sitter metric is a special form of the non-static Friedmann metric, and appears to be genuinely non-static since it describes the initial exponential expansion of the Big Bang universe. However, the de Sitter metric appears to be perfectly static in the Schwarzschild frame where the vacuum fluid is supposed to be in motion. Here we highlight the conflicts between the static and non-static versions of the de-Sitter metric from a physical perspective. In particular, while the "Principle of Energy Conservation" is honored in one case, the same is badly violated for the other. However, we offer a partial resolution of such conflicts by deriving the static de Sitter metric by solving the relevant field equations. It is seen that, it is the very special vacuum equation of state pressure = -density which results in the static form even when the vacuum fluid is supposed to be in motion.

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.