Powershell - Global variable inside function

Question

I have the following script which queries a remote users SID:

$target = Read-Host "Enter the address of the target machine"
$global:user = Read-Host "Enter the username to be added to the ACL"
$cred = Get-Credential

$sid = Invoke-Command -ComputerName $target -Credential $cred -ScriptBlock {
function get-sid
{
    Param ( $DSIdentity )
    $ID = new-object System.Security.Principal.NTAccount($DSIdentity)
    return $ID.Translate( [System.Security.Principal.SecurityIdentifier] ).toString()
}
get-sid $global:user
}
$sid

However, for some reason the $global:user is not accessible inside the function. It throw this error:

A constructor was not found. Cannot find an appropriate constructor for type System.Security.Principal.NTAccount.
    + CategoryInfo          : ObjectNotFound: (:) [New-Object], PSArgumentException
    + FullyQualifiedErrorId : CannotFindAppropriateCtor,Microsoft.PowerShell.Commands.NewObjectCommand
    + PSComputerName        : target-win
 
You cannot call a method on a null-valued expression.
    + CategoryInfo          : InvalidOperation: (:) [], RuntimeException
    + FullyQualifiedErrorId : InvokeMethodOnNull
    + PSComputerName        : target-win

If I remove the variable in the function and simply put get-sid "TheActualUserName" then the script works and the sid is returned. What am I missing? Is 'global' not being used? Why not.