Strong Gravity

In this talk I will describe numerical constructions of gravitational
duals of theories deformed by localized Dirac delta sources for scalar
operators. We perform two different constructions, one at zero and
the other at nonzero temperature. Surprisingly we find that imposing the preservation of scale
invariance at zero temperature requires the bulk scalar self-interaction potential to be
the one found in a certain Kaluza-Klein compactification of 11D supergravity.
The gravitational setup seems a-priori to be quite unusual and challenging
from the numerical relativity perspective.

Using holography, we study the evolution of a spatially homogeneous, far from equilibrium, strongly coupled N=4 supersymmetric Yang-Mills plasma with a non-zero charge density or a background magnetic field. This gauge theory problem corresponds, in the dual gravity description, to an initial value problem in Einstein-Maxwell theory with homogeneous but anisotropic initial conditions. We explore the dependence of the equilibration process on different aspects of the initial departure from equilibrium and, while controlling for these dependencies, examine how the equilibration dynamics are affected by the presence of a non-vanishing charge density or an external magnetic field. The equilibration dynamics are remarkably insensitive to the addition of even large chemical potentials or magnetic fields, the equilibration time is set primarily by the form of the initial departure from equilibrium. For initial deviations from equilibrium which are well localized in scale, we formulate a simple model for equilibration times which agrees quite well with our results.

We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order  even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more `rigid'.  Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.

Scalar fields are a useful proxy for other complex interactions, but also an attractive extension of General Relativity and a possible dark matter component. I will discuss some aspects of the gravitational interaction of scalar fields, in particular (i) the formation and growth of self-gravitating structures and their interaction with compact stars. and (ii) superradiance around black holes and how it can be used to constraint particle masses.

We study a general class of D-dimensional spacetimes that admit a non-twisting and shear-free null vector field. This includes the famous non-expanding Kundt family and the expanding Robinson-Trautman family of spacetimes. In particular, we show that the algebraic structure of the Weyl tensor is I(b) or more special, and derive surprisingly simple conditions under which the optically privileged null direction is a multiple WAND. All possible algebraically special types, including the refinement to subtypes, are thus identified. No field equations are applied, so that the results are valid not only in Einstein's theory but also in its generalizations. Differences between the D=4 and D>4 cases are summarized, and we give a short discussion of some interesting particular subcases (exact gravitational waves, gyratons, non-rotating p-form black holes etc.).

We discuss a problem of a black hole formation in the ghost-free gravity. We demonstrate how a non-local modification of gravity equations regularizes static and dynamical solutions. We focus on the problem of a collapse of small masses in the ghost-free gravity, and demonstrate that there exists a mass gap for mini-black-hole formation in this model.

The known basic building blocks of matter, the quarks and leptons, come in three generations or flavors.
The masses and interactions of the different flavors show a very hierarchical structure and the origin of these hierarchies remains an unsolved mystery of particle physics. The same hierarchies lead to a very high sensitivity of flavor changing processes to new undiscovered particles even outside the reach of direct searches at particle colliders.
In this colloquium I will present recent developments in constructing a theory of flavor and highlight the complementarity of flavor, Higgs, and collider physics in searching for new phenomena at the TeV scale and beyond.

A modified gravity (MOG) theory has been developed over the past decade that can potentially fit all the available data in cosmology and the present universe. The basic ingredients of the theory are described by an action principle determined by the Einstein-Hilbert metric tensor and curvature tensor. An additional massive vector field φµ is sourced by a gravitational charge $Q=\sqrt{\alpha G_N}M$, where $\alpha$ is a parameter, $G_N$ is Newton's gravitational constant and $M$ is the mass of a body. In addition, two scalar fields $G(x)$ and $\mu(x)$ are added to the action principle, where $G(x)$ describes a variable $G_N$ and $\mu$ is the effective mass-range parameter of the the vector field $\phi_\mu$. For a slow moving test particle in a weak gravitational field, a modified Newtonian acceleration law is derived. This acceleration law reduces to the Newtonian acceleration law for distance scales $d << \mu^{-1}$. This acceleration law is applied to predict the rotation curves of galaxies and globular clusters with excellent fits to data for $\alpha=8.89\pm 0.34$ and $\mu=0.042\pm 0.004\,{\rm kpc}^{-1}$ without dark matter. An application to galaxy clusters with the same values of $\alpha$ and $\mu$ results in fits to cluster dynamics data without dark matter. The colliding clusters "bullet cluster" is also explained without dark matter. The vector field $\phi_\mu$ coupling to standard model particles is of gravitational strength and the mass of the vector field is $m_\phi=2.6\times 10^{-28}\,eV$. This makes the vector field undetectable in the present universe. 

For early universe cosmology before the formation of stars and galaxies, the mass $m_\phi$, determined by the scalar field $\mu(x)$, is bigger, $m_\phi >> 2.6\times 10^{-28}\,eV$, and can act as an ultralight cold dark matter photon with gravitational strength coupling to matter. The modified gravity can fit the cosmological data up to the epoch when stars and galaxies are first formed, and when the $\phi_\mu$ field density $\rho_\phi$ is significantly diluted compared to the baryon density $\rho_b$. After the commencement of the star and galaxy formation epoch, the modified gravity without dark matter takes over. A prediction of the matter power spectrum is made of the first formation of galaxies that do not have dark matter halos. The lack of detectability of the gravitationally sourced dark photon can explain why no convincing detection has so far been made of dark matter particles in laboratory and satellite experiments.

The modified gravity theory vacuum field equations with a smooth vector field source energy-momentum tensor are solved to produce a black hole that differs from the Schwarzschild, Kerr and Reissner-Norstr\"om black holes when the parameter $\alpha\neq 0$. A modified gravity solution is also obtained from a nonlinear regular vector field solution that is regular at $r=0$. This solution can describe a black hole with two horizons as well as a no black hole solution with no horizon. The black hole MOG solutions possess a photosphere and they cast a shadow against a bright background. The sizes and deformations of these shadows can be detected by the VLBI and Event Horizon (EHT) project. These observations will be able to test general relativity for strong gravitational fields.  A traversable wormhole can be constructed using the modified gravity theory with a wormhole throat stabilized by the gravitationally sourced repulsive vector field.  

Calculations in General Relativity inevitably involve tricky manipulations of tensor equations. In many cases, the tensor algebra involved is at best tedious and fraught with error, and at worst impossible. It is, however, ideally suited to implementation in a computer algebra system such as Mathematica. In this talk I will show how the xAct tensor algebra package can be used to make light work of difficult tensor calculations. I will illustrate its wide-reaching functionality using applications in my own research, with relevance to black hole perturbations, numerical relativity and quantum gravity.

Surprisingly, several basic questions in classical and quantum gravity, which were resolved some 40-50 years ago for zero $\Lambda$, still remain open in the $\Lambda >0$ case. In particular, for $\Lambda >0$, we still do not have a satisfactory notion of gravitational radiation or Bondi 4-momentum in exact general relativity, nor a positive energy theorem. Similarly, the standard constructions of `in' and `out' Hilbert spaces that we routinely use (e.g. in the analysis of black hole evaporation) do not extend to the $\Lambda >0$ case. In this talk I will present some illustrative examples of these quandaries and introduce a systematic approach to resolve the open issues.

 

The Kerr metric of vacuum general relativity is expected to describe astrophysical black holes. Boson stars, on the other hand, are one of the simplest gravitating solitons, suggested as astrophysical compact objects, black holes mimickers and as dark matter candidates. Kerr black holes with scalar hair, found in [1], continuously interpolate between these two types of, per se, physically interesting solutions. I will describe the construction of these solutions and discuss theoretical, astrophysical and high energy physics aspects and challenges for Kerr black holes with scalar hair.

References:

[1] Kerr black holes with scalar hair, Carlos A. R. Herdeiro, Eugen Radu, Phys. Rev. Lett. 112 (2014) 221101; e-Print: arXiv:1403.2757

[2] A new spin on black hole hair, C. Herdeiro, E. Radu, International Journal of Modern Physics D 23 (2014) 1442014; e-Print: arXiv: 1405.3696;

[3] Construction and physical properties of Kerr black holes with scalar hair, C. Herdeiro and E. Radu, arXiv:1501.04319 [gr-qc]; Focus Issue on "Black holes and fundamental fields" to appear in Classical and Quantum Gravity