Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneralized Relativistic Wave Equations with Intrinsic Maximum Momentum
332
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
rate research
Read More
We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable non-equilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time tau_0. As a consequence, the stress-energy tensor acquires non-trivial quantum corrections to the classical free-streaming form.
We study the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. Using the holographic complexity=action (CA) and complexity=volume (CV) proposals, we study the full time dependence of complexity and the complexity of formation for two dimensional states dual to rotating BTZ. The obtained results and their dependence on angular momentum turn out to be analogous to those of charged states dual to Reissner-Nordstrom AdS black holes. For CA, our computation carefully accounts for the counterterm in the gravity action, which was not included in previous analysis in the literature. This affects the complexity early time dependence and its effect becomes negligible close to extremality. In the grand canonical ensemble, the CA and CV complexity of formation are linear in the temperature, and diverge with the same structure in the speed of light angular velocity limit. For CA the inclusion of the counterterm is crucial for both effects. We also address the problem of studying holographic complexity for higher dimensional rotating black holes, focusing on the four dimensional Kerr-AdS case. Carefully taking into account all ingredients, we show that the late time limit of the CA growth rate saturates the expected bound, and find the CV complexity of formation of large black holes diverges in the critical angular velocity limit. Our holographic analysis is complemented by the study of circuit complexity in a two dimensional free scalar model for a thermofield double (TFD) state with angular momentum. We show how this can be given a description in terms of non-rotating TFD states introducing mode-by-mode effective temperatures and times. We comment on the similarities and differences of the holographic and QFT complexity results.
The fluid/gravity correspondence establishes how gravitational dynamics, as dictated by Einsteins field equations, are related to the fluid dynamics, governed by the relativistic Navier-Stokes equations. In this work the correspondence is extended, where the duality between incompressible fluids and gravitational backgrounds with soft hair excitations is implemented. This construction is set through appropriate boundary conditions to the gravitational background, leading to a correspondence between generalized incompressible Navier-Stokes equations and soft hairy horizons.
The gravitational shock waves have provided crucial insights into entanglement structures of black holes in the AdS/CFT correspondence. Recent progress on the soft hair physics suggests that these developments from holography may also be applicable to geometries beyond negatively curved spacetime. In this work, we derive a remarkably simple thermodynamic relation which relates the gravitational shock wave to a microscopic area deformation. Our treatment is based on the covariant phase space formalism and is applicable to any Killing horizon in generic static spacetime which is governed by arbitrary covariant theory of gravity. The central idea is to probe the gravitational shock wave, which shifts the horizon in the $u$ direction, by the Noether charge constructed from a vector field which shifts the horizon in the $v$ direction. As an application, we illustrate its use for the Gauss-Bonnet gravity. We also derive a simplified form of the gravitational scattering unitary matrix and show that its leading-order contribution is nothing but the exponential of the horizon area: $mathcal{U}=exp(i text{Area})$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
