General Relativity and Quantum Cosmology (gr-qc)

Abstract: We cut a general, static, spherically symmetric spacetime which satisfying generalized Birkhoff's theorem and paste its copy to make a wormhole with a thin shell of any barotropic fluid in general relativity and we investigate the stability of the thin shell on a throat against linearized spherically symmetric perturbations. We show that the stability of the thin-shell wormhole satisfying a transparency condition which prohibits its momentum flux passing through the throat is characterized by circular photon orbits called (anti-)photon sphere in the original spacetime.

Abstract: We show that the maximal globally hyperbolic solution of the initial-value problem for the higher-dimensional vacuum Einstein equations on two transversally intersecting characteristic hypersurfaces contains a future neighborhood of the hypersurfaces.

Abstract: We finish the proof of the no-hair theorem for stationary, analytic, connected, suitably regular, four dimensional vacuum black holes. We show how to define the surface gravity and the angular velocity of horizons without assuming analyticity. We point out that, under the usual regularity conditions, vacuum near-horizon geometries are Kerrian without assuming analyticity.

Abstract: I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether a given theory is the final one or not. This is relevant for both canonical quantum gravity and string theory.

Abstract: We explore an interesting connection between black hole shadow parameters and the acceleration bounds for radial linear uniformly accelerated (LUA) trajectories in static spherically symmetric black hole spacetime geometries. For an incoming radial LUA trajectory to escape back to infinity, there exists a bound on its magnitude of acceleration and the distance of closest approach from the event horizon of the black hole. We calculate these bounds and the shadow parameters, namely the photon sphere radius and the shadow radius, explicitly for specific black hole solutions in $d$-dimensional Einstein's theory of gravity, in pure Lovelock theory of gravity and in the $\mathcal{F}(R)$ theory of gravity. We find that for a particular boundary data, the photon sphere radius $r_{ph}$ is equal to the bound on radius of closest approach $r_b$ of the incoming radial LUA trajectory while the shadow radius $r_{sh}$ is equal to the inverse magnitude of the acceleration bound $|a|_b$ for the LUA trajectory to turn back to infinity. Using the effective potential technique, we further show that the same relations are valid in any theory of gravity for static spherically symmetric black hole geometries of the Schwarzschild type.

Abstract: The Event Horizon Telescope has recently observed the images and shadows of the compact objects M87$^*$ and Sgr A$^*$ at the centres of the galaxies Messier 87 and Milky Way. This has opened up a new window in observational astronomy to probe and test gravity and fundamental physics in the strong-field regime. In this paper, we consider a rotating version of a modified Janis-Newman-Winicour metric, study its shadow, and constrain the metric parameters using the observed shadows of M87$^*$ and Sgr A$^*$. Depending on parameter values, the spacetime metric represents either a naked singularity or a wormhole. We find that the naked singularity case is not consistent with observations, as it casts a shadow which is much smaller than the observed ones. On the other hand, the shadow formed by the wormhole branch, depending on the parameter values, is consistent with the observations. We put constraints on the wormhole throat radius by comparing the shadow with the observed ones of M87$^*$ and Sgr A$^*$.

Abstract: We explore the existence of wormholes in the context of $f(R,T)$ gravity. The $f(R,T)$ theory is a curvature-matter coupled modified gravity that depends on an arbitrary function of the Ricci scalar $R$ and the trace of the stress-energy tensor $T$. In this work, we adopt two different choices for the matter Lagrangian density ($\mathcal{L}_m= \mathcal{P}$ and $\mathcal{L}_m= p_r$) and investigate the impact of each one on wormhole structure. By adequately specifying the redshift function and the shape function, we found a variety of exact wormhole solutions in the theory. Our finding indicates that, for both classes of wormholes the energy density is always positive throughout the spacetime, while the radial pressure is negative. This means exotic matter is necessary for the existence of wormholes in $f(R,T)$ gravity.

Abstract: In this article we investigate the cumulative stochastic gravitational wave spectra as a tool to gain insight on the creation mechanism of primordial black holes. We consider gravitational waves from the production mechanism of primordial black holes and from the gravitational interactions of those primordial black holes among themselves and other astrophysical black holes. We specifically focus on asynchronous bubble nucleation during a first order phase transition as the creation mechanism. We have used two benchmark phase transitions through which the primordial black holes and the primary gravitational wave spectra have been generated. We have considered binary systems and close hyperbolic interactions of primordial black holes with other primordial and astrophysical black holes as the source of the secondary part of the spectra. We have shown that this unique cumulative spectra have features which directly and indirectly depend on the specifics of the production mechanism.

Abstract: In the Standard Model of particle physics, the mass of the Higgs particle can be linked to the scale at which the Standard Model breaks down due to a Landau pole/triviality problem: for a Higgs mass somewhat higher than the measured value, the Standard Model breaks down before the Planck scale. We take a first step towards investigating this relation in the context of causal set quantum gravity. We use a scalar-field propagator that carries the imprints of spacetime discreteness in a modified ultraviolet behavior that depends on a nonlocality scale. We investigate whether the modification can shift the scale of the Landau pole in a scalar field theory with quartic interaction. We discover that the modifications speed up the onset of the Landau pole considerably, so that the scale of new physics occurs roughly at the nonlocality scale. Our results call into question, whether a separation between the nonlocality scale and the discreteness scale, which is postulated within causal set quantum gravity, and which has been argued to give rise to phenomenological consequences, is in fact achievable. Methodologically, our paper is the first to apply continuum functional Renormalization Group techniques in the context of a causal-set inspired setting.

Abstract: Nonlocal gravity (NLG), a classical extension of Einstein's theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay, we discuss the local limit of NLG and apply this limit to the expanding homogenous and isotropic universe. The theory only allows spatially flat cosmological models; furthermore, de Sitter spacetime is forbidden. The components of the model will have different dynamics with respect to cosmic time as compared to the standard $\Lambda$CDM model; specifically, instead of the cosmological constant, the modified flat model of cosmology involves a dynamic dark energy component in order to account for the accelerated phase of the expansion of the universe.