There are important indications that nature may be locally finite-dimensional, i.e., that any spatially bounded subsystem can be described by a finite-dimensional local observable algebra. Motivated by these ideas, we show that operational spacetime topology is described by an atomistic Boolean algebra if (i) local observable algebras are finite-dimensional factors, (ii) the intersection of two local algebras is also local, and (iii) the commutant of a local algebra is also local. Thus, in this case, spacetime has a point-free granular behavior at small scales.
We argue that de Sitter universes with a small cosmological constant are entropically favored to have three spatial dimensions. The conclusion relies on the causal-patch description of de Sitter space, where fiducial observers experience local thermal equilibrium up to a stretched horizon, on the holographic principle, and on some assumptions about the nature of gravity and the constituents of Hawking/Unruh radiation.
On a Pregeometric Origin for Spacetime Dimensionality and Metric Structure
出于惠勒的自下而上pregeometric，我们介绍了一个pregeometric方法，不假设惠勒的概率幅建立时空邻域。相反，一个非平凡的度量是通过一致性基的概念产生的，一致性基是由离散拓扑群在一些任意的基本的可数集上产生的。我们展示了我们的一致性基础的元素的随行乘法的概念，反映了基本的组结构。然后利用这一事实来创建最大长度的环境序列，从而获得精细的度量结构。由此产生的度量结构，对于某些组结构，与E4-嵌入图一致。提供了Z2 X Z4、D4、Z6、D3、Z 8和Z5上的示例。讨论了Z7和Q8上的欧氏嵌入性。与图论中典型的统计方法不同，该方法在低阶集合上生成维度。在Z2 x Z2 x Z4的背景下，提供了可能的应用程序的量子随机性和非局域性/不可分离性，波函数崩溃，和时空的M4结构的前几何建模。
We report an investigation of the Snyder noncommutative spacetime and of some of its most natural generalizations, also looking at them as a powerful tool for comparing different notions of dimensionality of a quantum spacetime. It is known that (generalized-)Snyder noncommutativity, while having rich off-shell implications (kinematical Hilbert space), does not affect on-shell particles (physical Hilbert space), and we argue that physically meaningful notions of dimensionality should describe such spacetimes as trivially four-dimensional, without any running with scales. By studying the thermo…
In the framework of gravothermal evolution of an ideal monatomic fluid, I examine the dynamical instability of the fluid sphere in ($N$+1) dimensions by exploiting Chandrasekhar's criterion to each quasistatic equilibrium along the sequence of the evolution. Once the instability is triggered, it would probably collapse into a black hole if no other interaction halts the process. From this viewpoint, the privilege of (3+1)-dimensional spacetime is manifest, as it is the marginal dimensionality in which the ideal monatomic fluid is stable but not too stable. Moreover, it is the unique dimensiona…
The relativistic equations of hydrostatic equilibrium for a spherically symmetric star, or the Tolman-Oppenheimer-Volkoff equations are known in higher dimensions. In this paper, these equations have been expressed in terms of parameters of 4 dimensional spacetime and solved numerically for 4, 5, 6, and 7 dimensions using a standard equation of state for the neutron star matter derived for the 4 dimensional spacetime. It has been shown that with the increase of the dimensionality, the maximum value of the mass of the neutron star decreases and the stars become less compact. Thus, although the …
Chaos bound violation by spinning particles in Gauss-Bonnet-AdS black holes
School of Mathematics, Physics and Statistics, Sichuan Minzu College（四川民族学院数理统计学院）；School of Physics and Astronomy, China West Normal University（西华师范大学物理与天文学院）
In this note, I derive the Chandrasekhar instability of a fluid sphere in ($N$+1)-dimensional Schwarzschild-Tangherlini spacetime and take the homogeneous (uniform energy density) solution for illustration. Qualitatively, the effect of positive (negative) cosmological constant tends to destabilize (stabilize) the sphere. In the absence of cosmological constant, the privileged position of (3+1)-dimensional spacetime is manifest in its own right. As it is the marginal dimensionality in which a monatomic ideal fluid sphere is stable but not too stable to trigger the onset of gravitational collaps…
Among the many disparate approaches towards quantum gravity, the reduction of spacetime dimension in the ultraviolet regime is expected to be a common thread. The dimensionality of spacetime can be defined in various contexts. The spectral dimension of spacetime is defined in the context of diffusion processes on a manifold. We show that a spacetime with zero-point length has spectral dimension $3.5$ when the characteristic diffusion time has the size of the zero-point length. The spectral dimension (negatively) diverges for an even shorter diffusion time, thus preventing any reliable physical…
We show that the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity $\mathcal{I}^-$ contains the whole of the future conformal infinity $\mathcal{I}^+$ in $(2+1)$ and $(3+1)$ dimensional Schwarzschild spacetimes, this property (which we call the Penrose property) does not hold for $(d+1)$ dimensional Schwarzschild if $d>3$. We also show that the Penrose property holds for the Kerr solution in $(3+1)$ dimensions, and discuss the connection with scattering theory in the presence of positive ma…
Using a lattice equation of state combined with the D-dimensional Tolman-Oppenheimer-Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a $2+1$ dimensional spacetime, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a $3+1$ dimensional spacetime, self-gravity lead…
