Relativistic Fluids and the Coupling of Gravity to Other Forces

相对论流体和重力与其他力的耦合

基本信息

项目摘要

The proposer will continue his investigations in two areas:i) shock-waves in Einstein's Theory of General Relativity withapplications to cosmology and ii) the coupling of Einstein's equations for the gravitational field to other (fundamental) force fields; for example to electromagnetism and nuclear forces.In part i) he will investigate his alternative model to the standard "Big-Bang" cosmology. In this theory, the observable universe began with a shock wave explosion into a stationary (time-independent) space. This explosion created the expanding universe that astronomers observe today. The leading edge of this expansion is modeled by an outward propagating shock-wave. Since shock-waves are irreversible solutions of the equations, information about the past is lost as the shock-wave advances. In this model one should therefore not expect a unique time reversal of the solution all the way back to an initial Big-Bang, whereby the entire universe was compressed into a tiny region. In part ii) the proposer will study how solutions of the equations of Quantum Mechanics change when gravity is taken into account. Up to now, gravity has been ignored in elementary particle theory, because gravity is much weaker than nuclear forces and electromagnetism. Preliminary calculations of the proposer show that in spite of the weakness of the gravitational force, the addition of gravity into the equations has a "smoothing"effect on solutions, and greatly modifies some aspects of elementary particle theory.The proposer will do research in two areas. First, he will investigate analternative scenario to the standard "Big-Bang" cosmology. In his model the observable universe began with a shock-wave explosion ratherthan from an incredibly dense small region the size of a grapefruit. Consistent with some recent astronomical observations of huge energy bursts in the very outer regions of the cosmos, this theory implies that there may be other distant universes which also arise from shock-wave explosions. Secondly, the proposer will study the effect that gravity has on other forces (electromagnetism and nuclear forces). Since the gravitational force is extremely weak in comparison to these other forces, physicists have ignored gravity in studying elementary particles. However, the proposer has found that the inclusion of gravity does actually play a role in elementary particle theory. Furthermore, he will investigate the possibility that quantum-theoretic effects play a role in the study of black holes.
提议者将继续在两个领域进行研究:i)爱因斯坦广义相对论中的冲击波及其在宇宙学中的应用;ii)爱因斯坦引力场方程与其他(基本)力场的耦合;例如电磁力和核力。在第一部分中,他将研究标准“大爆炸”宇宙学的替代模型。 在这个理论中,可观测的宇宙始于冲击波爆炸进入静止(与时间无关)的空间。 这次爆炸创造了天文学家今天观察到的不断膨胀的宇宙。这种膨胀的前缘是通过向外传播的冲击波来模拟的。 由于冲击波是方程的不可逆解,因此随着冲击波的前进,有关过去的信息就会丢失。因此,在这个模型中,人们不应该期望解决方案会出现独特的时间反转,一直回到最初的大爆炸,即整个宇宙被压缩成一个很小的区域。 在第二部分中,提议者将研究当考虑重力时量子力学方程的解如何变化。 到目前为止,引力在基本粒子理论中一直被忽略,因为引力比核力和电磁力弱得多。 提出者的初步计算表明,尽管引力很弱,但在方程中加入引力对解具有“平滑”作用,并且极大地修改了基本粒子理论的某些方面。提出者将在两个领域进行研究。 首先,他将研究标准“大爆炸”宇宙学的另一种情况。 在他的模型中,可观测的宇宙是从冲击波爆炸开始的,而不是从柚子大小的极其密集的小区域开始的。与最近对宇宙最外层区域巨大能量爆发的一些天文观测相一致,这一理论意味着可能存在其他遥远的宇宙也是由冲击波爆炸产生的。 其次,提议者将研究重力对其他力(电磁力和核力)的影响。 由于与其他力相比,引力极其微弱,物理学家在研究基本粒子时忽略了引力。然而,提出者发现,引力确实在基本粒子理论中发挥了作用。 此外,他还将研究量子理论效应在黑洞研究中发挥作用的可能性。

项目成果

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Joel Smoller其他文献

Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials
Cosmology with a Shock-Wave
An existence theorem for positive solutions of semilinear elliptic equations
On the Oppenheimer‐Volkoff Equations in General Relativity
Symmetry-breaking for positive solutions of semilinear elliptic equations

Joel Smoller的其他文献

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{{ truncateString('Joel Smoller', 18)}}的其他基金

Mathematical Questions in Gravitation, Black Holes, Cosmology, and Rotating Stars
引力、黑洞、宇宙学和旋转恒星的数学问题
  • 批准号:
    1105189
  • 财政年份:
    2011
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Nonlinear Partial Differential Equations and Applications to Fluid Dynamics, General Relativity and Geometry
非线性偏微分方程及其在流体动力学、广义相对论和几何中的应用
  • 批准号:
    0963846
  • 财政年份:
    2011
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Mathematical Questions Resulting from the Coupling of Gravity to Other Fields
重力与其他场耦合产生的数学问题
  • 批准号:
    0603754
  • 财政年份:
    2006
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Differential Equations resulting from the interaction of Gravity with other Force Fields, and Shock-Waves in General Relativity
由重力与其他力场相互作用产生的微分方程以及广义相对论中的冲击波
  • 批准号:
    0103998
  • 财政年份:
    2001
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problemss in Relativistic Fluids andEinstein-Yang/Mills Equations
数学科学:相对论流体和爱因斯坦-杨/米尔斯方程中的问题
  • 批准号:
    9501128
  • 财政年份:
    1995
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems In Differential Equations And General Relativity
数学科学:微分方程和广义相对论中的问题
  • 批准号:
    9203972
  • 财政年份:
    1992
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems in Nonlinear Partial Differential Equations
数学科学:非线性偏微分方程问题
  • 批准号:
    9003337
  • 财政年份:
    1991
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Problems in Nonlinear Partial Differential Equations
数学科学:非线性偏微分方程问题
  • 批准号:
    8905205
  • 财政年份:
    1989
  • 资助金额:
    $ 12万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Problems in Nonlinear Partial Differential Equations
数学科学:非线性偏微分方程问题
  • 批准号:
    8600035
  • 财政年份:
    1986
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Problems in Partial Differential Equations
数学科学:偏微分方程问题
  • 批准号:
    8301243
  • 财政年份:
    1983
  • 资助金额:
    $ 12万
  • 项目类别:
    Continuing Grant

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