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Whether the space-time is curved or not? The experimental criterions to judge this point are: (1) The results of three classical relativistic experiments in essence are favorable to the special relativistic gravitational theory (base in the flat space-time). However they are unfavorable to the general relativity. (2) In the Gravity Probe-B experiment: the gyroscope precession rate of the orbital effect deduced from the special relativistic gravitational theory =(2/3)* the precession rate of geodetic effect deduced from the general relativity, the precession rate of the earth rotation effect deduced from the special relativistic gravitational theory =(3/2)* the square of cos(phi)* the precession rate of the frame-dragging effect deduced from the general relativity, where (phi) is the angle between the projection of gyroscope angular velocity in the equatorial plane and the normal line of orbital plane. If the experimental values are identical with the predictive values deduced from the special relativistic gravitational theory, then the space-time is flat.
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Can we obtain the predictive value of GP-B experiment direct from the well known experimental results? This predictive value is more reliable then that deduced from special model of theory. In this paper, we calculate in this way. The result is same as that from special relativistic gravitational theory. So it is extremely likely that GP-B experiment will prove space-time is flat.
We study the motion of neutral and charged spinning bodies in curved space-time in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation which allows for different choices of the hamiltonian. We derive conditions for the existence of constants of motion and apply the formalism to the case of spherically symmetric space-times. We show that the periastron of a spinning body in a stable orbit in a Schwarzschild or Reissner-Nordstr{o}m background not only precesses, but also varies radially. By analysing the stability conditions for circular motion we find the innermost stable circular orbit (ISCO) as a function of spin. It turns out that there is an absolute lower limit on the ISCOs for increasing prograde spin. Finally we establish that the equations of motion can also be derived from the Einstein equations using an appropriate energy-momentum tensor for spinning particles.
Conversion of vacuum fluctuations into real particles was first predicted by L. Parker considering an expanding universe, followed in S. Hawkings work on black hole radiation. Since their experimental observation is challenging, analogue systems have gained attention in the verification of this concept. Here we propose an experimental set-up consisting of two adjacent piezoelectric semiconducting layers, one of them carrying dynamic quantum dots (DQDs), and the other being p-doped with an attached gate on top, which introduces a space-dependent layer conductivity. The propagation of surface acoustic waves (SAWs) on the latter layer is governed by a wave equation with an effective metric. In the frame of the DQDs, this space- and time-dependent metric possesses a sonic horizon for SAWs and resembles that of a two dimensional non-rotating and uncharged black hole to some extent. The non-thermal steady state of the DQD spin indicates particle creation in form of piezophonons.
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them covariant with respect to nonlinear transform of variables. In this work, we construct rigorous and covariant formulations of time-slicing path integrals for quantum and classical stochastic dynamics in curved space. We first establish a rigorous criterion for correct time-slice actions of path integrals (Lemma 1). This implies the existence of infinitely many equivalent representations for time-slicing path integral. We then show that, for any dynamics with second order generator, all time-slice actions are asymptotically equivalent to a Gaussian (Lemma 2). Using these results, we further construct a continuous family of equivalent actions parameterized by an interpolation parameter $alpha in [0,1]$ (Lemma 3). The action generically contains a spurious drift term linear in $Delta boldsymbol x$, whose concrete form depends on $alpha$. Finally we also establish the covariance of our path-integral formalism, by demonstrating how the action transforms under nonlinear transform of variables. The $alpha = 0$ representation of time-slice action is particularly convenient because it is Gaussian and invariant, as long as $Delta boldsymbol x$ transforms according to Itos formula.
We examine two far-reaching and somewhat heretic consequences of General Relativity. (i) It requires a cosmology which includes a preferred rest frame, absolute space and time. (ii) A rotating universe and time travel are strict solutions of General Relativity.
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