Session X7: Alternate Theories of Gravity

Derivation of Einstein--Cartan theory from general relativity

General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein--Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein--Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein--Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincar\'{e} symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein--Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein--Cartan theory is relevant.   

String-inspired Infinite Derivative theories of Gravity

In String Theory there often appears a rather interesting class of higher derivative theories containing an infinite set of derivatives in the form of an exponential. These theories may provide a way to tame ultra-violet divergences without introducing ghost-like states. In this talk we provide a brief overview on the progress that has been made over the last decade to construct such infinite derivative theories of gravity. We will mostly focus on the status of the classical singularities, viz. Big Bang and the Black hole singularities, but we will also briefly discuss the recent progress that has been made on understanding quantum aspects of such infinite derivative theories. In the process we will present some general results that can be applied to any covariant torsion-free metric theory of gravity.   

Black Hole Formation in Randall-Sundrum Braneworld II

We present the results from a numerical study of the gravitational collapse of a massless scalar field within the framework of the Randall-Sundrum II braneworld model. The calculations are fully coupled so that the nonlinear dynamics of the brane, the matter confined to it, and the bulk, are all treated self-consistently. We show that evolutions of sufficiently strong initial configurations of scalar field generate black holes which extend into the bulk and which overall have spherical topology. Using distinct initial data sets that result in black holes with similar physical properties, we find preliminary evidence for a no-hair property for the black holes in this scenario. Additionally, we show that the black hole solutions generated from the dynamical system, are consistent with those recently computed from a static ansatz applied to the vacuum model.   

Slowly-Rotating Black Hole Solution in Einstein-Dilaton-Gauss-Bonnet Gravity

We present a stationary and axisymmetric black hole solution in Einstein-Dilaton-Gauss-Bonnet gravity to quadratic order in the ratio of the spin angular momentum to the black hole mass squared. This solution introduces new corrections to previously found nonspinning and linear-in-spin solutions. The location of the event horizon and the ergosphere are modified, as well as the quadrupole moment. The new solution is of Petrov type I, although lower order in spin solutions are of Petrov type D. There are no closed timelike curves or spacetime regions that violate causality outside of the event horizon in the new solution. We calculate the modifications to the binding energy, Kepler's third law, and properties of the innermost stable circular orbit. These modifications are important for determining how the electromagnetic properties of accretion disks around supermassive black holes are changed from those expected in general relativity.   

Requirements for a Manifestly Covariant Quantum Field Theory

Quantum field theory has shown much success in defining manifestly covariant fields in Minkowski space-time. The general procedure for construction of QFT in terms of annihilation and creation operators acting through a simplectic form is outlined. It is demonstrated that this methodology fails to define a general covariant vector field in a space-time spanning a Riemannian manifold with Lorentz metric (M,g$_{\mathrm{uv}})$; therefore, no appropriate outer product can be defined to produce a general 2$^{\mathrm{nd}}$ rank tensor (i.e. stress-energy tensor). The QFT defined in flat space-time is expanded to include curvilinear coordinates. The manifestly covariant QFT in curved space-time is used to redefine the equations of motion in terms of the classical field theory. The resulting theory has the benefit of requiring an S-matrix defining unitarily equivalent quantum theories while providing an exact formulation for the quantized equations of motion in a gravitational field. The physical implications of this construction are discussed including the anisomorphic nature of the simplectic vector space in curvilinear coordinates. An example involving plane wave expansion is discussed.   

The Newtonian approximation in Causal Dynamical Triangulations

I review how to derive Newton's law of universal gravitation from the Weyl strut between two Chazy-Curzon particles. I also briefly review Causal Dynamical Triangulations (CDT), a method for evaluating the path integral from canonical quantum gravity using Regge calculus and restrictions of the class of simplicial manifolds evaluated to those with a defined time foliation, thus enforcing a causal structure. I then discuss how to apply this approach to Causal Dynamical Triangulations, in particular modifying the algorithm to keep two simplicial submanifolds with curvature (i.e. mass) a fixed distance from each other, modulo regularized deviations and across all time slices. I then discuss how to determine if CDT produces an equivalent Weyl strut, which can then be used to obtain the Newtonian limit. I wrap up with a brief discussion of computational methods and code development.   

Gravitational radiation from compact binaries in scalar-tensor gravity

General relativity (GR) has been extensively tested in the solar system and in binary pulsars, but never in the strong-field, dynamical regime. Soon, gravitational-wave (GW) detectors like Advanced LIGO will be able to probe this regime by measuring GWs from inspiraling and merging compact binaries. One particularly interesting alternative to GR is scalar-tensor gravity. We present the calculation of tensor and scalar waveforms for inspiraling compact binaries in a general class of scalar-tensor theories. The waveforms are constructed using a standard GR method known as ``Direct Integration of the Relaxed Einstein equations,'' appropriately adapted to the scalar-tensor case. The tensor waveforms are calculated to second post-Newtonian (2PN) order, where ``0PN'' is equivalent to the lowest order GR result. The scalar waveforms are calculated to 1.5PN order. We also calculate to 1PN order the rate at which both tensor and scalar waves carry energy away from the system.   

Image Comparisons of Black Hole vs. Neutron Dark Star by Ray Tracing

In previous papers we have discussed the concept of a theory of gravitation with local energy conservation, and the properties of a large neutron star resulting when the energy of gravitation resides locally with the particle mass and not in the gravitational field. A large neutron star's surface radius grows closer to the gravitational radius as the mass increases. Since the localization of energy applies to the photon, they do not decrease energy rising in a gravitational field, and can escape. Photon trajectories in a strong gravitational field can be investigated by the use of ray tracing procedures. Only a fraction of the blackbody radiation emitted from the surface escapes into space (about 0.00004{\%} for Sag A*). Because of the low {\%} of escaping radiation, the heavy neutron stars considered in this paper will be referred to as a Neutron Dark Star (NDS). In contrast to the Black Hole (BH) which should be totally dark inside the photon shadow, the NDS will appear as a fuzzy low luminosity ball. For Sag A* a full width half maximum diameter is about 3.85 Schwarzschild radii inside the shadow. (http://www.arxdtf.org/css/Image{\%}20Comparisons.pdf ). The Event Horizon Telescope should be able to distinguish the difference between the theories.   

Experimental signatures of semiclassical gravity and the many-body Schr\"odinger-Newton equation

In semiclassical gravity, the many-body Schr\"odinger-Newton (SN) equation, which governs the evolution of a many-particle system under self gravity, predicts that classical and quantum eigenfrequencies of a macroscopic mechanical oscillator are different. For high-$Q$ and low-frequency ($\sim$10s of mHz) torsional pendulums made with atoms with small internal motion fluctuations, such as Tungsten or Platinum, this difference can be considerably larger than the classical eigenfrequency of the pendulum. We exploit this split in the design of an optomechanics experiment which, in contrast with experiments that test for quantum gravity, is feasible with current technology and which distinguishes, at low temperatures and within about a year, between the predictions of the SN equation and standard quantum mechanics. Specifically, we propose using light to probe the motion of such oscillators. Moreover, the nonlinearity induced by the SN equation forces us to revisit the wavefunction collapse postulate, resulting in two proposed prescriptions for how the measurement of the light is performed. Each predict a noticeable feature in the spectrum of the outgoing light that is separate from the features of classical force noise.