Data Reduction And Error Analysis For The Physical Sciences

One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

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Testing general relativity with present and future astrophysical observations

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories

The universe is so much bigger than the bit we can see in our observable bubble   and we know nothing about what lies out there in the cosmos. The challenge is so  much bigger than is shown on this chart and it is evident that we really only  understand a tiny fraction of the whole cosmos.  Theories ​for Dark Energy have been around for a long time but we still have no  satisfactory explanation. None of the theories are adequate, some are clearly wrong    – an error of 10^120 is a really big miss!  Scott Dodelson of Carnegie Mellon University, one of the lead scientists behind the  Dark Energy Survey’s new map of cosmic structure says:

Dark Energy

Some recently discovered nonperturbative strong-field effects in tensor-scalar theories of gravitation are interpreted as a scalar analogue of ferromagnetism: "spontaneous scalarization." This phenomenon leads to very significant deviations from general relativity in conditions involving strong gravitational fields, notably binary-pulsar experiments. Contrary to solar-system experiments, these deviations do not necessarily vanish when the weak-field scalar coupling tends to zero. We compute the scalar "form factors" measuring these deviations, and notably a parameter entering the pulsar timing observable $\ensuremath{\gamma}$ through scalar-field-induced variations of the inertia moment of the pulsar. An exploratory investigation of the confrontation between tensor-scalar theories and binary-pulsar experiments shows that nonperturbative scalar field effects are already very tightly constrained by published data on three binary-pulsar systems. We contrast the probing power of pulsar experiments with that of solar-system ones by plotting the regions they exclude in a generic two-dimensional plane of tensor-scalar theories.

Tensor-Scalar Gravity and Binary-Pulsar Experiments

The purpose of the current Letter is to give some relations between gravitational lensing in the strong-deflection limit and the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. On the one side, the relations obtained can give a physical interpretation of the strong-deflection limit parameters. On the other side, they also give an alternative method for the measurement of the frequencies of the quasinormal modes of spherically symmetric, asymptotically flat black holes. They could be applied to the localization of the sources of gravitational waves and could tell us what frequencies of the gravitational waves we could expect from a black hole acting simultaneously as a gravitational lens and a source of gravitational waves.

Connection between black-hole quasinormal modes and lensing in the strong deflection limit.

Recent results show that when nonlinear electrodynamics is considered, the no-scalar-hair theorems in the scalar–tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented.1,2 What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to nonlinear electrodynamics in a special class of scalar–tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar–tensor theories considered, the black holes have a single, non-degenerate horizon, i.e. their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.

Phases of 4d scalar–tensor black holes coupled to born–infeld nonlinear electrodynamics

In some models dark energy is described by phantom scalar fields (scalar fields with the ``wrong'' sign of the kinetic term in the Lagrangian). In the current paper we study the effect of phantom scalar field and/or phantom electromagnetic field on gravitational lensing by black holes in the strong deflection regime. The black-hole solutions that we have studied have been obtained in the frame of the Einstein-(anti-)Maxwell-(anti)dilaton theory. The numerical analysis shows a considerable effect of the phantom scalar and electromagnetic fields on the angular position, brightness, and separation of the relativistic images.

Gravitational lensing by phantom black holes

In the present paper, we study the scalar sector of the quasinormal modes of charged general relativistic, static, and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. We find that for a certain domain of the parametric space, there exists unstable quasinormal modes. The presence of instabilities implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero modes. We prove that such scalar-tensor black holes really exist by solving the full system of scalar-tensor field equations for the static, spherically symmetric case. The obtained solutions for the hairy black holes are nonunique, and they are in one-to-one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the nonunique hairy black holes is also examined, and we find that the solutions for which the scalar field has zeros are unstable against radial perturbations. The paper ends with a discussion of possible formulations of a new classification conjecture.

Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

The nonexistence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with a nontrivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of nonlinear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type nonlinear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the general relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, nondegenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.

Ivan Zh. Stefanov

Papers

Connection between black-hole quasinormal modes and lensing in the strong deflection limit.

Phases of 4d scalar–tensor black holes coupled to born–infeld nonlinear electrodynamics

Gravitational lensing by phantom black holes

Quasinormal modes, bifurcations, and nonuniqueness of charged scalar-tensor black holes

Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics